.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/photochem/quantum_yield/plot_02_stark_einstein_photochemical_equivalence.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_photochem_quantum_yield_plot_02_stark_einstein_photochemical_equivalence.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_photochem_quantum_yield_plot_02_stark_einstein_photochemical_equivalence.py:


Stark-Einstein law: one absorbed photon, at most one reacting molecule
========================================================================

The law of photochemical equivalence (Stark 1908, Einstein 1912-1913)
says each absorbed quantum activates exactly one molecule. The quantum
yield :math:`\Phi` (moles product / moles photons absorbed), computed by
:func:`~chemistrykit.photochem.photochemical_quantum_yield`, then equals
1 for an ideal one-photon, one-molecule reaction and is less than 1 when
the excited molecule has other ways to lose its energy.

.. GENERATED FROM PYTHON SOURCE LINES 14-37

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.photochem import photochemical_quantum_yield, photons_absorbed

    # Photons absorbed over a series of exposures (Beer-Lambert, A = 0.8).
    I0, A = 1.0e-6, 0.8
    t = np.linspace(0.0, 1000.0, 11)
    n_photons = photons_absorbed(I0, A) * t

    # Product formed if every activated molecule reacts (efficiency 1), or if
    # 60% of activated molecules decay back without reacting.
    fig, ax = plt.subplots()
    for efficiency in (1.0, 0.4):
        n_product = efficiency * n_photons
        ax.plot(n_photons * 1e6, n_product * 1e6, "o-", label=rf"$\Phi$ = {efficiency}")
    ax.plot(n_photons * 1e6, n_photons * 1e6, "k:", label=r"Stark-Einstein limit, $\Phi=1$")
    ax.set_xlabel(r"Photons absorbed ($\mu$einstein)")
    ax.set_ylabel(r"Product formed ($\mu$mol)")
    ax.set_title("Photochemical equivalence: product vs. photons absorbed")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/photochem/quantum_yield/images/sphx_glr_plot_02_stark_einstein_photochemical_equivalence_001.png
   :alt: Photochemical equivalence: product vs. photons absorbed
   :srcset: /api/gallery/photochem/quantum_yield/images/sphx_glr_plot_02_stark_einstein_photochemical_equivalence_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 38-39

The quantum yield is the slope of that line.

.. GENERATED FROM PYTHON SOURCE LINES 39-43

.. code-block:: Python

    Phi = photochemical_quantum_yield(0.4 * n_photons[1:], n_photons[1:])
    print("Quantum yield at every exposure:", np.round(Phi, 6))

    plt.show()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Quantum yield at every exposure: [0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4]





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.038 seconds)


.. _sphx_glr_download_api_gallery_photochem_quantum_yield_plot_02_stark_einstein_photochemical_equivalence.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_stark_einstein_photochemical_equivalence.ipynb <plot_02_stark_einstein_photochemical_equivalence.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_stark_einstein_photochemical_equivalence.py <plot_02_stark_einstein_photochemical_equivalence.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_stark_einstein_photochemical_equivalence.zip <plot_02_stark_einstein_photochemical_equivalence.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_